Problem: Reduce to lowest terms: $ \dfrac{5}{9} \div - \dfrac{8}{9} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{8}{9}$ is $- \dfrac{9}{8}$ Therefore: $ \dfrac{5}{9} \div - \dfrac{8}{9} = \dfrac{5}{9} \times - \dfrac{9}{8} $ $ \phantom{ \dfrac{5}{9} \times - \dfrac{9}{8}} = \dfrac{5 \times -9}{9 \times 8} $ $ \phantom{ \dfrac{5}{9} \times - \dfrac{9}{8}} = \dfrac{-45}{72} $ The numerator and denominator have a common divisor of $9$, so we can simplify: $ \dfrac{-45}{72} = \dfrac{-45 \div 9}{72 \div 9} = -\dfrac{5}{8} $